# Reflecting boundary condition posed as a Riemann problem

I am trying to implement a solver for the Euler/Navier Stokes equations. I have a problem implementing boundary conditions for the wall. I am using an unstructured solver.

A lot of literature says that at the wall you simply reflect the normal velocity, and then pose it as a Riemann problem. So let me take the momentum equation. The U here is $\rho u$. The F (flux) is $\rho u^2+p$. $u$ is velocity, $\rho$ is density, $p$ is pressure. Assume that the grid is such that $u$ is normal velocity.

Now, the way literature guides toward implementing this boundary condition is to take ghost values such that boundary conditions at the wall are satisfied. So reflect the velocity, and copy density, pressure.

The velocity will come to zero at the wall using this. But if you look at the flux, it will not. I have compared Lax-Friedrichs, HLL and I don't see how F becomes $p$ as it should.

Any help?

For reference I will put up this link

http://arc.aiaa.org/doi/abs/10.2514/6.2014-2923

• The correct boundary condition is zero normal velocity at the wall, not zero momentum flux. Commented Jan 4, 2021 at 9:54